Fibonacci128 Flex Bracelet

Posted August 1, 2023

Table of Contents

Details

Fibonacci128 Flex Bracelet is a beautiful flexible PCB with 128 SK9822-EC20 HDR RGB LEDs surface mounted in a Fibonacci distribution.

It consists of 128 SK9822-EC2020 HDR (High Dymanic Range) RGB LEDs, arranged into a Fermat’s spiral pattern.

It has solder pads on the back that match the pinout of a Pixelblaze V3 Pico by ElectroMage. It can be used by any microcontroller via the 5V, GND, Clock and Data In pins.

In disc phyllotaxis, as in the sunflower and daisy, the mesh of spirals occurs in Fibonacci numbers because divergence (angle of succession in a single spiral arrangement) approaches the golden ratio. The shape of the spirals depends on the growth of the elements generated sequentially. In mature-disc phyllotaxis, when all the elements are the same size, the shape of the spirals is that of Fermat spirals—ideally. That is because Fermat's spiral traverses equal annuli in equal turns. The full model proposed by H Vogel in 1979[2] is

r = c \sqrt{n},
\theta = n \times 137.508^\circ,

where θ is the angle, r is the radius or distance from the center, and n is the index number of the floret and c is a constant scaling factor. The angle 137.508° is the golden angle which is approximated by ratios of Fibonacci numbers.[3]

Fermat's spiral. (2015, October 24). In Wikipedia, The Free Encyclopedia. Retrieved 02:45, February 24, 2016, from https://en.wikipedia.org/w/index.php?title=Fermat%27s_spiral

Specifications

  • Size: 6.18 x 2.80 x .004 inch (157.0 x 71.25 x 0.11 mm)
  • 2 layer printed circuit board
  • Flex PCB with yellow coverlay
  • ENIG (electroless nickel immersion gold) Finish
  • Designed in the US by Evil Genius Labs
  • Some are assembled in the US by Evil Genius Labs

Pixelblaze Map

Pixelblaze is an advanced WiFi LED pattern engine, created by ElectroMage. Live pattern expression compiler, lightning fast fixed point math, and HDR!

Fibonacci boards are laid out physically in a zig-zag pattern, from center to edge and back to center, all the way around the board. This layout automatically makes one dimensional patterns designed for strips visually interesting.

To treat the board as a matrix, you can use a pixel map. A 2D XY map can allow you to scroll colors, palettes, and patterns across the panel horizontally, vertically, diagonally, etc.

This map can be copied and pasted into the Pixel Mapper in the Mapper tab of your Pixelblaze web interface.

View in LED Mapper

[[84.52,25.68],[105.01,27.61],[114.22,31.11],[120.79,35.58],[125.71,40.79],[129.33,46.57],[119.97,44.86],[115.07,39.08],[107.93,33.77],[95.99,28.83],[100.31,34.28],[108.65,40.96],[113.7,47.49],[107.1,48.5],[101.64,40.82],[89.58,30.7],[93.84,37.77],[100.41,47.66],[93.79,44.49],[87.17,37.37],[85.94,44.52],[82.25,31.96],[79.68,41.23],[74.5,45.69],[68.03,47.4],[76.67,35.36],[70.15,39.53],[61.06,46.63],[26.26,47.78],[20.46,44.41],[15.14,40.15],[12.08,25.52],[16.28,30.95],[21.13,35.64],[26.59,39.5],[32.61,42.4],[39.2,44.2],[46.36,44.7],[54.26,43.51],[63.47,39.8],[69.52,32.74],[57.16,37.31],[48.25,38.27],[40.71,37.35],[34.08,35.07],[28.23,31.69],[23.12,27.4],[18.75,22.31],[15.14,16.56],[12.31,10.25],[17.22,1.96],[19.39,8.45],[22.41,14.45],[26.31,19.87],[31.1,24.58],[36.81,28.42],[43.58,31.19],[51.76,32.57],[62.54,31.8],[73.38,27.15],[57.09,27.96],[47.79,26.01],[40.71,22.69],[35.06,18.37],[30.57,13.27],[27.12,7.54],[24.66,1.32],[32.7,1.73],[35.73,7.75],[39.97,13.26],[45.65,18.13],[53.34,22.15],[65.05,24.99],[60.43,20.08],[51.55,15],[45.66,9.45],[41.59,3.47],[51.93,7.15],[58.33,13.69],[70.35,21],[66.19,14.89],[58.62,6.61],[65.58,8.26],[78.1,22.39],[72.98,13.28],[67.68,1.75],[73.64,6.42],[79.06,15.88],[80.89,8.11],[85.55,3.3],[85.74,12.8],[91.5,8.58],[140.09,5.16],[134.07,2.25],[106.31,2.69],[98.09,7.62],[86.23,19.77],[94.07,15.26],[104.78,9.29],[113.2,7.02],[120.7,6.73],[127.56,7.91],[133.87,10.29],[139.61,13.68],[144.77,17.98],[142.56,26.42],[137.82,21.72],[132.34,17.86],[126.11,15.01],[119.05,13.37],[110.92,13.29],[100.85,15.62],[92.61,21.7],[106.74,18.82],[115.94,19.28],[123.35,21.41],[129.57,24.75],[134.81,29.04],[139.14,34.12],[142.61,39.85],[145.2,46.11],[137.63,46.88],[134.68,40.9],[130.72,35.46],[125.67,30.73],[119.36,26.87],[111.33,24.17],[100,23.22]]